Introduction to Process Control Second Edition Jose A. Romagnoli Ahmet Palazoglu CRC Press Taylor & Francis Group Boca Raton London NewYork CRC Press is an imprint of the Taylor & Francis Group, an informa business
Contents Preface Authors Introduction -xix xxiii xxv PART I Introduction Chapter 1 Why Process Control? 3 1.1 Historical Background 4 1.2 Role of Control in Process Industries 5 1.2.1 Traditional Role of Process Control 5 1.2.2 Expanded Role of Process Control 7 1.3 Objectives of Control 8 1.3.1 What about Performance? 10 1.3.2 Economic Benefits of Control 10 1.4 Summary 11 Continuing Problem 11 Solution 12 References 12 _ Chapter 2 Definitions and Terminology 13 2.1 Concepts and Definitions 13 2.2 Control Design Problem 19 2.3 Control System Design 23 2.4 Control Design Project 24 2.4.1 Preliminary Engineering 25 2.4.2 Detailed Engineering 26 2.4.3 Implementation 26 2.4.4 Installation 26 2.4.5 Commissioning 26 2.4.6 First Production Start-Up and Turnover 26 2.4.7 Training 27 2.5 Summary 27 Continuing Problem 27 Solution 27 Reference 28 ix
x Contents Part I Summary 29 Additional Reading 29 Exercises 30 References 39 PART II Modeling for Control Chapter 3 Basic Concepts in Modeling 43 3.1 Why Is Process Modeling Necessary? 44 3.1.1 Application Areas and Benefits 44 3.1.2 Goal of Modeling 45 3.2 Classification of Models 46 3.2.1 Linear versus Nonlinear 46 3.2.2 Distributed Parameter versus Lumped Parameter 48 3.2.3 Deterministic versus Stochastic 49 3.3 Types of Models 49 3.3.1 Models Based on Source of Information 50 3.3.2 Models Based on Mathematical Representation 50 3.3.2.1 State-Space Models 50 3.3.2.2 Input-Output Models 51 3.4 Degrees of Freedom 54 3.5 Models and Control 56 3.6 Summary 57 References 57 Chapter 4 Development of Models from Fundamental Laws 59 4.1 Principles of Modeling 59 4.2 Models Based on Fundamental Laws 60 4.2.1 Constitutive Relations 63 4.2.2 Steady-State Condition 64 4.3 Modeling of Processes Involving Chemical Reactions 68 4.4 Modeling of Complex Systems 71 4.5 Distributed Parameter Systems 74 4.6 Numerical Solution of Model Equations 78 4.7 Summary 81 Continuing Problem 81 Solution 81 References 84 Chapter 5 Input-Output Models 85 5.1 Linear (Linearized) Model 85 5.1.1 Deviation Variables 86
Contents Xl 5.1.2 Higher Dimensional Equations 89 5.1.3 Linear State-Space Model 91 5.2 Concept of Transfer Function 93 5.3 Transfer Functions of Single-Input Single-Output Processes 94 5.3.1 Asymptotic Theorems 96 5.3.1.1 Initial Value Theorem 96 5.3.1.2 Final Value Theorem 96 5.4 Properties of Transfer Functions 97 5.5 Nonrational Transfer Functions 100 5.6 Summary 102 Continuing Problem 103 Solution 103 Chapter 6 Models from Process Data 107 6.1 Development of Empirical Models 107 6.1.1 Steps in Developing Empirical Models 107 6.1.1.1 Performing the Experiments 108 6.1.1.2 Building the Model 109 6.1.1.3 Evaluating the Model 109 6.2 Model Structures 110 6.3 Process Reaction Curve Method Ill 6.4 Regression in Modeling 118 6.4.1 Linear Regression 118 6.4.2 Nonlinear Regression 120 6.5 Summary 124 Continuing Problem 124 References 126 Part II Summary 127 Additional Reading 127 Exercises 128 References 140 PART III Process Analysis Chapter 7 Stability 143 7.1 Stability of Linear Systems 143 7.2 Input-Output Stability 147 7.3 Routh's Criterion 150 7.4 Root-Locus Method 152
xjj Contents 7.5 Direct Substitution Method 153 7.6 Summary 155 References 155 Chapter 8 Dynamic Performance 157 8.1 Input Types 157 8.2 First-Order Processes 158 8.2.1 Special Case: Integrating Processes 161 8.3 Second-Order Processes 162 8.3.1 Special Case: Step Response of Underdamped Processes 164 8.4 Multicapacity Processes 167 8.4.1 Special Case: Interacting Processes 171 8.5 Effect of Zeros 173 8.5.1 Special Case: Right Half-Plane Zeros 175 8.6 Effect of Time Delays 176 8.7 Summary 179 Continuing Problem 179 Chapter 9 Frequency Response 181 9.1 What Is Frequency Response? 181 9.2 Complex Numbers in Polar Coordinates 182 9.3 Construction of Frequency Response 183 9.4 Evaluation of Frequency Response 185 9.5 Frequency Response of Common Systems 188 9.6 Bode Diagrams 189 9.7 Nyquist Diagrams 193 9.8 Systems in Series 196 9.9 Summary 198 Continuing Problem 199 Part III Summary Additional Reading Exercises Reference 201 201 202 207 PART IV Feedback Control Chapter 10 Basic Elements of Feedback Control 211 10.1 Feedback Control Problem 211 10.2 Control Law 215 10.2.1 Proportional Mode 215
Contents xiii 10.2.2 Integral Mode 216 10.2.3 Derivative Mode 216 10.2.4 Three-Mode Controller (PID) 216 10.2.4.1 Special Case: Discrete PID 217 10.2.5 Physical Realizability 217 10.3 Closed-Loop Transfer Functions 218 10.4 Analysis of Individual Terms in PID Controllers 221 10.4.1 Proportional Mode 221 10.4.2 Integral Mode 224 10.4.3 Derivative Mode 226 10.4.4 Integral Windup 227 10.5 Practical Issues in PID Design 228 10.5.1 Direct and Reverse Action 228 10.5.2 Bumpless Transfer 229 10.5.3 PID Equation Forms 229 10.5.3.1 Interacting/Noninteracting 229 10.5.3.2 Derivative on Error/Derivative on Measurement 229 10.5.3.3 Positional/Velocity 230 10.6 Summary 230 Continuing Problem 230 Solution 231 Reference 233 Chapter 11 Stability Analysis of Closed-Loop Processes 235 11.1 Closed-Loop Stability 235 11.2 Routh's Criterion 237 11.2.1 Dealing with Delays 239 11.3 Root-Locus Method 240 11.3.1 Zeros at Infinity 243 11.4 Modeling Errors 244 11.5 Frequency Response Methods 246 11.6 Summary 249 Continuing Problem 249 Solution 250 Chapter 12 Feedback Control Design 255 12.1 Design Objectives 255 12.1.1 Response-Based Criteria 255 12.1.2 Error-Based Criteria 256 12.2 Controller Tuning Techniques 259 12.2.1 Open-Loop Tuning (Cohen-Coon) Method 259
xiv Contents 12.2.2 Closed-Loop Timing (Ziegler-Nichols) Method 261 12.2.3 Direct Synthesis Method 265 12.2.3.1 Processes without Time Delay 267 12.2.3.2 Processes with Time Delay 267 12.3 Comparing the Methods 270 12.4 Summary 272 Continuing Problem 273 Solution 273 References 277 Part IV Summary 279 Additional Reading 279 Exercises 280 PART V Model-Based Control Chapter 13 Model-Based Control 289 13.1 Feedforward Control 289 13.1.1 Feedforward-Feedback Control Strategy 291 13.1.2 Implementation Aspects 293 13.2 Delay Compensation (Smith Predictor) 295 13.3 Internal Model Control 300 13.3.1 Concept of Perfect Control 302 13.3.2 IMC Design Procedure 303 13.3.3 PID Tuning Using IMC Rules 304 13.4 Summary 306 Continuing Problem 306 Solution 306 References 313 Chapter 14 Model Uncertainty and Robustness 315 14.1 IMC Structure with Model Uncertainty 315 14.2 Description of Model Uncertainty 316 14.2.1 Additive Uncertainty 316 14.2.2 Multiplicative Uncertainty 317 14.2.3 Estimation of Uncertainty Bounds 317 14.3 IMC Design under Model Uncertainty 319 14.3.1 Robust Stability 320 14.3.2 Robust Performance 321 14.4 Summary 326 References 326
Contents xv Chapter 15 Model Predictive Control 327 15.1 General Principles 327 15.1.1 Model Forms 329 15.1.1.1 Impulse-Response Models 329 15.1.1.2 Step-Response (Convolution) Models 329 15.1.1.3 State-Space Models 330 15.2 Dynamic Matrix Control 330 15.2.1 Single-Input-Single-Output Unconstrained DMC Problem 333 15.2.2 Controller Tuning 334 15.3 Process Constraints 336 15.4 State-Space Formulation of MPC 337 15.4.1 Infinite Horizon Problem 338 15.5 Summary 339 Continuing Problem 340 Solution 340 References 342 Part V Summary 343 Additional Reading 343 Exercises 344 PART VI Multivariate Control Chapter 16 Multivariable Systems 351 16.1 Cascade Control 351 16.2 Ratio Control 354 16.2.1 Ratio Computation 355 16.2.2 Set-Point Computation 356 16.3 Split-Range Control 359 16.4 Override Control 360 16.5 Summary 362 Continuing Problem 362 Solution 363 References 368 Chapter 17 Multivariable Systems 369 17.1 Characteristics of Multivariable Processes 369 17.2 Modeling of Multivariable Processes 370
xvi Contents 17.3 Transfer Functions of Multivariable Processes 377 17.3.1 Poles and Zeros of MIMO Systems 380 17.4 Multivariable Feedback Control Structure 384 17.4.1 Closed-Loop Poles and Zeros 385 17.4.2 Stability of MIMO Closed-Loop Systems 386 17.5 Summary 390 Continuing Problem 390 References 395 Chapter 18 Design of Multivariable Controllers 397 18.1 Multiple-Input-Multiple-Output Feedback Analysis 397 18.1.1 LoopF,,-^ 398 18.1.2 Loopft.-*B 399 18.2 RGA Interaction Measure 402 18.2.1 Selection of Loops 405 18.3 Multiloop Controller Design 408 18.4 Design of Noninteracting Control Loops: Decouplers 409 18.5 Summary 414 Continuing Problem 414 Solution 415 References 419 Part VI Summary 421 Additional Reading 421 Exercises 422 References 428 PART VII Control in Modern Manufacturing Chapter 19 Practical Control of Nonlinear Processes 431 19.1 Operating Regime Modeling Approach 431 19.1.1 Global Model Structure 433 19.2 Gain-Scheduling Controller 437 19.2.1 Determination of Process Gains 439 19.2.2 Gain-Scheduling Implementation 439 19.3 Multimodel Controller Design 444 19.3.1 Multimodel Predictive Control (MMPC) 444 19.4 Summary 447 References 448
Contents xvii Chapter 20 Process Optimization and Control 449 20.1 Process Optimization 449 20.1.1 Objective Function 450 20.1.2 Constraints.451 20.1.2.1 Equality Constraints 451 20.1.2.2 Inequality Constraints 451 471 20.2 Optimizing Control of Disturbances 456 20.2.1 Open-Loop Back-Off 457 20.2.2 Closed-Loop Back-Off 461 20.3 Dynamic Optimization and Transition Planning 466 20.4 Summary 470 References Chapter 21 Industrial Control Technology 473 21.1 Evolution of Industrial Control Technology 473 21.2 Generic Industrial Control Systems Architecture 474 21.2.1 Supervisory Environment 475 21.2.2 Control Environment 476 21.2.3 Communication Environment 476 21.2.4 Data Exchange 476 21.3 Summary 490 Continuing Problem 490 References 493 Chapter 22 Role of Process Control in Modern Manufacturing 495 22.1 Expanded Role of Control in Modern Manufacturing 495 22.1.1 LayerJ Control 496 22.1.2 Layer_2 Control 497 22.1.3 Layer_3 Control 497 22.2 Model-Centric Technologies 504 22.3 Integrated Control Systems 507 22.4 Summary 513 References 513 Chapter 23 Data Processing and Reconciliation 515 23.1 Dealing with Missing Points 515 23.2 Outliers 518 23.3 Characterizing Process Data 520 23.4 Modeling 23.4.1 Model Fitting Based on Least-Squares Estimation 524 Process Data 522 23.5 Data Reconciliation 525
xviii Contents 23.6 Issues in Data Reconciliation 528 23.6.1 Process Model 528 23.6.2 Classification of Process Variables 530 23.6.3 Linear Data Reconciliation with Unmeasured Variables 532 23.6.4 Gross Errors 533 23.7 Data Reconciliation and Model-Centric Technologies 534 23.8 Summary 539 References 539 Chapter 24 Process Monitoring 541 24.1 Process Monitoring 541 24.2 Statistical Process Control 542 24.2.1 Univariate Control Charts 543 24.2.2 Control Chart Interpretation 544 24.2.3 Multivariate Charts 545 24.3 Principal Component Analysis 546 24.3.1 Calculation of Principal Components 546 24.4 Multivariate Performance Monitoring 551 24.4.1 Elliptical Normal Operation Region 553 24.4.2 T2 and Squared Prediction Error Charts 555 24.4.3 Contribution Plots 556 24.5 Fault Diagnosis 24.6 Controller Performance Monitoring 563 and Classification 556 24.6.1 State Classification 564 24.6.2 Model Validation 564 24.6.3 Stochastic Performance Monitoring 565 24.6.4 Controller Oscillation Assessment 566 24.7 Summary 567 References 567 Part VII Summary 569 Additional Reading 569 Exercises 572 Appendix A: Linearization 577 Appendix B: Laplace Transformation 585 Appendix C: Matrix Operations 593 Appendix D: Basic Statistics 601 Index 609